DEV BHOOMI INSTITUE OF TECHNOLOGY DEHRADUN Department Of Computer Application. Design and Analysis of Algorithms Lab MCA-302

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1 DEV BHOOMI INSTITUE OF TECHNOLOGY DEHRADUN Department Of Computer Application Design and Analysis of Algorithms Lab MCA-302 1

2 INDEX S.No. PRACTICAL NAME DATE PAGE NO. SIGNATURE 1. Write a Program to Implement Insertion Sort in C programming language 2. Write a Program to implement quick sort in C programming language. 3. Write a Program to Implement Merge Sort in C programming language. 4. Write a Program to Implement Heap sort in C programming language. 5. Write a Program to Implement Bubble Sort in C programming language 6. Write a Program to Implement Searching: Sequential and Binary Search. 7. Write a Program to Implement Searching: Sequential and Binary Search. 8. Write a Program to implement Dynamic programming traveling sales person problem). 9. Write a Program to implement Back tracking (nqueens problem). 10. Write a Program to implement Back tracking (Hamiltonian cycles). 2

3 EXPERIMENT NO-1 Objective:Write a Program to Implement Insertion Sort in C programming language Program: #include <stdio.h> #define MAX 7 void insertion_sort(int *); void main() int a[max], i; printf("enter elements to be sorted:"); for (i = 0;i<MAX;i++) scanf("%d", &a[i]); insertion_sort(a); printf("sorted elements:\n"); for (i = 0;i< MAX; i++) printf(" %d", a[i]); /* sorts the input */ void insertion_sort(int * x) int temp, i, j; for (i = 1;i<MAX;i++) temp = x[i]; j = i - 1; while (temp < x[j] && j >= 0) x[j + 1] = x[j]; 3

4 j = j - 1; x[j + 1] = temp; Output: enter elements to be sorted: sorted elements:

5 EXPERIMENT NO-2 Objective:Write a Program to implement quick sort in C programming language. Program: # include <stdio.h> # include <conio.h> # include <time.h> void Exch(int *p, int *q) int temp = *p; *p = *q; *q = temp; void QuickSort(int a[], int low, int high) inti, j, key, k; if(low>=high) return; key=low; i=low+1; j=high; while(i<=j) while ( a[i] <= a[key] ) i=i+1; while ( a[j] > a[key] ) j=j-1; if(i<j) Exch(&a[i], &a[j]); Exch(&a[j], &a[key]); QuickSort(a, low, j-1); QuickSort(a, j+1, high); void main() int n, a[1000],k; clock_tst,et; 5

6 double ts; clrscr(); printf("\n Enter How many Numbers: "); scanf("%d", &n); printf("\nthe Random Numbers are:\n"); for(k=1; k<=n; k++) a[k]=rand(); printf("%d\t",a[k]); st=clock(); QuickSort(a, 1, n); et=clock(); ts=(double)(et-st)/clocks_per_sec; printf("\nsorted Numbers are: \n "); for(k=1; k<=n; k++) printf("%d\t", a[k]); printf("\nthe time taken is %e",ts); getch(); OUTPUT: Enter size of the array: 5 Enter 5 elements: Sorted elements:

7 EXPERIMENT NO-3 Objective:Write a Program to Implement Merge Sort in C programming language. Program: #include<stdio.h> #include<stdlib.h> void Merge(int a[], inttmp[], intlpos, intrpos, int rend) inti, lend, n, tmppos; lend = rpos - 1; tmppos = lpos; n = rend - lpos + 1; while(lpos<= lend &&rpos<= rend) if(a[lpos] <= a[rpos]) tmp[tmppos++] = a[lpos++]; else tmp[tmppos++] = a[rpos++]; while(lpos<= lend) tmp[tmppos++] = a[lpos++]; while(rpos<= rend) tmp[tmppos++] = a[rpos++]; for(i = 0; i< n; i++, rend--) a[rend] = tmp[rend]; 7

8 void MSort(int a[], inttmp[], int left, int right) int center; if(left < right) center = (left + right) / 2; MSort(a, tmp, left, center); MSort(a, tmp, center + 1, right); Merge(a, tmp, left, center + 1, right); void MergeSort(int a[], int n) int *tmparray; tmparray = malloc(sizeof(int) * n); MSort(a, tmparray, 0, n-1); free(tmparray); main() inti, n, a[10]; printf("enter the number of elements :: "); scanf("%d",&n); printf("enter the elements :: "); 8

9 for(i = 0; i< n; i++) scanf("%d",&a[i]); MergeSort(a,n); printf("the sorted elements are :: "); for(i = 0; i< n; i++) printf("%d ",a[i]); printf("\n"); OUTPUT: Enter the number of elements :: 7 Enter the elements :: The sorted elements are ::

10 EXPERIMENT NO-4 Objective:Write a Program to Implement Heap sort in Cprogramming language. Program: #include<stdio.h> void create(int []); void down_adjust(int [],int); void main() intheap[30],n,i,last,temp; printf("enter no. of elements:"); scanf("%d",&n); printf("\nenter elements:"); for(i=1;i<=n;i++) scanf("%d",&heap[i]); //create a heap heap[0]=n; create(heap); //sorting while(heap[0] > 1) //swap heap[1] and heap[last] last=heap[0]; temp=heap[1]; 10

11 heap[1]=heap[last]; heap[last]=temp; heap[0]--; down_adjust(heap,1); //print sorted data printf("\narray after sorting:\n"); for(i=1;i<=n;i++) printf("%d ",heap[i]); void create(int heap[]) inti,n; n=heap[0]; //no. of elements for(i=n/2;i>=1;i--) down_adjust(heap,i); void down_adjust(int heap[],inti) intj,temp,n,flag=1; n=heap[0]; while(2*i<=n && flag==1) j=2*i; //j points to left child if(j+1<=n && heap[j+1] > heap[j]) 11

12 j=j+1; if(heap[i] > heap[j]) flag=0; else temp=heap[i]; heap[i]=heap[j]; heap[j]=temp; i=j; OUTPUT: Enter no. of elements:5 Enter elements: Array after sorting:

13 EXPERIMENT NO-5 Objective:Write a Program to Implement Bubble Sort in C programming language. Program: #include <stdio.h> intmain() intdata[100],i,n,step,temp; printf("enter the number of elements to be sorted: "); scanf("%d",&n); for(i=0;i<n;++i) printf("%d. Enter element: ",i+1); scanf("%d",&data[i]); for(step=0;step<n-1;++step) for(i=0;i<n-step-1;++i) if(data[i]>data[i+1]) /* To sort in descending order, change > to < in this line. */ temp=data[i]; data[i]=data[i+1]; data[i+1]=temp; printf("in ascending order: "); for(i=0;i<n;++i) printf("%d ",data[i]); return 0; 13

14 OUTPUT: Enter the number of elements to be sorted: 6 1. Enter element: Enter element: 3 3. Enter element: 0 4. Enter element: Enter element: 1 6. Enter element: -9 In ascending order:

15 EXPERIMENT NO-6 Objective:Write a Program to Implement Searching: Sequential and Binary Search. Program: #include <stdio.h> /* Function for sequential search */ void sequential_search(int array[], int size, int n) inti; for (i = 0; i< size; i++) if (array[i] == n) printf("%d found at location %d.\n", n, i+1); break; if (i == size) printf("not found! %d is not present in the list.\n", n); /* End of sequential_search() */ /* Function for binary search */ void binary_search(int array[], int size, int n) inti, first, last, middle; first = 0; last = size - 1; middle = (first+last) / 2; while (first <= last) if (array[middle] < n) first = middle + 1; else if (array[middle] == n) printf("%d found at location %d.\n", n, middle+1); break; 15

16 else last = middle - 1; middle = (first + last) / 2; if ( first> last ) printf("not found! %d is not present in the list.\n", n); /* End of binary_search() */ /* The main() begins */ intmain() inta[200], i, j, n, size; printf("enter the size of the list:"); scanf("%d", &size); printf("enter %d Integers in ascending order\n", size); for (i = 0; i< size; i++) scanf("%d", &a[i]); printf("enter value to find\n"); scanf("%d", &n); printf("sequential search\n"); sequential_search(a, size, n); printf("binary search\n"); binary_search(a, size, n); return 0; 16

17 OUTPUT: Enter the size of the list:10 Enter 10 Integers in ascending order Enter value to find 16 sequential search 16 found at location 5. Binary search 16 found at location 5 17

18 EXPERIMENT NO-7 Objective: Write a Program to implement Greedy method Fractional knapsack problem in C. Programs: #include<stdio.h> #include<time.h> #include<conio.h> void knapsack(float capacity, int n, float weight[], float profit[]) float x[20], totalprofit,y; inti,j; y=capacity; totalprofit=0; for(i=0;i <n;i++) x[i]=0.0; for(i=0;i <n;i++) if(weight[i] > y) break; else x[i]=1.0; totalprofit=totalprofit+profit[i]; y=y-weight[i]; if(i< n) x[i]=y/weight[i]; totalprofit=totalprofit+(x[i]*profit[i]); printf("the selected elements are:-\n "); for(i=0;i <n;i++) if(x[i]==1.0) printf("\nprofit is %f with weight %f ", profit[i], weight[i]); else if(x[i] > 0.0) 18

19 printf("\n%f part of Profit %f with weight %f", x[i], profit[i], weight[i]); printf("\ntotal profit for %d objects with capacity %f = %f\n\n", n, capacity,totalprofit); void main() float weight[20],profit[20],ratio[20], t1,t2,t3; int n; time_tstart,stop; float capacity; clrscr(); inti,j; printf("enter number of objects: "); scanf("%d", &n); printf("\nenter the capacity of knapsack: "); scanf("%f", &capacity); for(i=0;i <n;i++) printf("\nenter %d(th) profit: ", (i+1)); scanf("%f", &profit[i]); printf("enter %d(th) weight: ", (i+1)); scanf("%f", &weight[i]); ratio[i]=profit[i]/weight[i]; start=time(null); for(i=0;i <n;i++) for(j=0;j <n;j++) if(ratio[i] > ratio[j]) t1=ratio[i]; ratio[i]=ratio[j]; ratio[j]=t1; t2=weight[i]; weight[i]=weight[j]; weight[j]=t2; 19

20 t3=profit[i]; profit[i]=profit[j]; profit[j]=t3; knapsack(capacity,n,weight,profit); stop=time(null); printf("\nknapsack = %f\n", difftime(stop,start)); getch(); OUTPUT: Enter number of objects: 5 Enter the capacity of knapsack: 10 Enter 1(th) profit: 9 Enter 1(th) weight: 6 Enter 2(th) profit: 15 Enter 2(th) weight: 3 Enter 3(th) profit: 20 Enter 3(th) weight: 2 Enter 4(th) profit: 8 Enter 4(th) weight: 4 Enter 5(th) profit: 10 Enter 5(th) weight: 3 The selected elements are:- Profit is with weight Profit is with weight Profit is with weight part of Profit with weight Total profit for 5 objects with capacity 10 = Knapsack =

21 EXPERIMENT NO-8 Objective:Write a Program to implement Dynamic programming traveling sales person problem). Programs: #include<stdio.h> intary[10][10],completed[10],n,cost=0; void takeinput() inti,j; printf("enter the number of villages: "); scanf("%d",&n); printf("\nenter the Cost Matrix\n"); for(i=0;i <n;i++) printf("\nenter Elements of Row: %d\n",i+1); for( j=0;j <n;j++) scanf("%d",&ary[i][j]); completed[i]=0; printf("\n\nthe cost list is:"); for( i=0;i <n;i++) printf("\n"); for(j=0;j <n;j++) printf("\t%d",ary[i][j]); void mincost(int city) inti,ncity; completed[city]=1; printf("%d--->",city+1); ncity=least(city); if(ncity==999) 21

22 ncity=0; printf("%d",ncity+1); cost+=ary[city][ncity]; return; mincost(ncity); intleast(int c) inti,nc=999; int min=999,kmin; for(i=0;i <n;i++) if((ary[c][i]!=0)&&(completed[i]==0)) if(ary[c][i]+ary[i][c] < min) min=ary[i][0]+ary[c][i]; kmin=ary[c][i]; nc=i; if(min!=999) cost+=kmin; return nc; intmain() takeinput(); printf("\n\nthe Path is:\n"); mincost(0); //passing 0 because starting vertex printf("\n\nminimum cost is %d\n ",cost); return 0; 22

23 OUTPUT: Enter the number of villages: 4 Enter the Cost Matrix Enter Elements of Row: Enter Elements of Row: Enter Elements of Row: Enter Elements of Row: The cost list is: The Path is: 1 >3 >2 >4 >1 Minimum cost is 71 23

24 EXPERIMENT NO-9 Objective:Write a Program to implement Back tracking (n-queens problem). Programs: #include<stdio.h> #include<math.h> char a[10][10]; int n; void printmatrix() inti, j; printf("\n"); for (i = 0; i< n; i++) for (j = 0; j < n; j++) printf("%c\t", a[i][j]); printf("\n\n"); intgetmarkedcol(int row) inti; for (i = 0; i< n; i++) if (a[row][i] == 'Q') return (i); break; intfeasible(int row, int col) inti, tcol; for (i = 0; i< n; i++) tcol = getmarkedcol(i); if (col == tcol abs(row - i) == abs(col - tcol)) return 0; return 1; void nqueen(int row) inti, j; if (row < n) 24

25 for (i = 0; i< n; i++) if (feasible(row, i)) a[row][i] = 'Q'; nqueen(row + 1); a[row][i] = '.'; else printf("\nthe solution is:- "); printmatrix(); intmain() inti, j; printf("\nenter the no. of queens:- "); scanf("%d", &n); for (i = 0; i< n; i++) for (j = 0; j < n; j++) a[i][j] = '.'; nqueen(0); return (0); OUTPUT: Enter the no. of queens:- 4 The solution is:-. Q..... Q Q..... Q. The solution is:-.. Q. Q Q. Q.. 25

26 EXPERIMENT NO-10 Objective:Write a Program to implement Back tracking (Hamiltonian cycles). Programs: #include<stdio.h> #include<conio.h> #define MAX 25 int x[max]; void Next_Vertex(int G[MAX][MAX],intn,int k) int j; while(1) x[k]=(x[k]+1)%(n+1); if(x[k]==0) return; if(g[x[k-1]][x[k]]!=0) for(j=1;j<=k-1;j++) if(x[j]==x[k]) break; if(j==k) if((k<n) ((k==n)&&(g[x[n]][x[1]]!=0))) return; void H_Cycle(int G[][MAX],intn,int k) inti; while(1) Next_Vertex(G,n,k); if(x[k]==0) return; if(k==n) printf("\n"); 26

27 for(i=1;i<=n;i++) printf(" %d",x[i]); printf(" %d",x[1]); else H_Cycle(G,n,k+1); void main() inti,j,v1,v2,edges,n,g[max][max]; clrscr(); printf("\n\t Program for Hamiltonian Cycle "); printf("\n Enter the number of vertices of graph: "); scanf("%d",&n); for(i=1;i<=n;i++) for(j=1;j<=n;j++) G[i][j]=0; x[i]=0; printf("\n Enter the total number of edges: "); scanf("%d",&edges); for(i=1;i<=edges;i++) printf("\n Enter the edge: "); scanf("%d%d",&v1,&v2); G[v1][v2]=1; G[v2][v1]=1; x[1]=1; printf("\n Hamiltonian cycle...\n"); H_Cycle(G,n,2); getch(); 27

Sorting & Searching. Hours: 10. Marks: 16

Sorting & Searching. Hours: 10. Marks: 16 Sorting & Searching CONTENTS 2.1 Sorting Techniques 1. Introduction 2. Selection sort 3. Insertion sort 4. Bubble sort 5. Merge sort 6. Radix sort ( Only algorithm ) 7. Shell sort ( Only algorithm ) 8.